Nb-fuzzy metric spaces with topological properties and applications

Abstract

Our aim is to introduce the notion of Nb-fuzzy metric space (FMS). We also define quasi N-FMS, and pseudo Nb-FMS with examples and counterexamples and prove a decomposition theorem for pseudo Nb-FMS. We prove various theorems related to the convergence of sequences and analyze topology of symmetric Nb-FMS. At last, we provide an application of q-contraction mapping as a Banach contraction principle (BCP) in the structure of symmetric Nb-FMS and applied it in the solution of integral equations and linear equations.